On Bound State of Cooper Pair in Superconductors

Debnarayan Jana

Department of Physics, University of Calcutta

In this pedological article, we discuss about the boundedness of two electrons above the Fermi sphere in three dimensions interacting via an attractive interaction. These two electrons having equal opposite momenta and spin are known as Cooper pairs. According to the spin content of this composite particle, they behave approximately as Bosons and the pairs are essential ingredient to theory of superconductivity. We compute the bound state of energy of the pair when the electrons interact via (i) constant potential (ii) potential separable in two coordinates and (iii) delta function potential above the spherical Fermi surface. With the help of the eigenstate, we proceed further to compute the average radius of the Cooper pair and discuss its implication in theory of superconductivity. We also generalize the form of binding energy of Cooper pair in case of ellipsoidal Fermi surface.